Now, using the Lyddane-Sachs-Teller relation [1]} we can further estimate the temperature dependence of the dielectric function as \(\epsilon (T) \sim 1/\omega (T)^2\)  [2]}, [3]}, [4]}.
In Fig. 3(b), we compare with the experimental observed dielectric constants by fixing the value of the dielectric function at zero temperature to the experimental one and using the temperature dependent FES frequency calculated above.
The characteristic flat plateau up to 4K and the subsequent drop in the dielectric function is reproduced very well by our PBE calculations.
Similar calculation with LDA do not follow the correct trend, highlighting the failure of LDA at describing the correct potential energy landscape for the FES mode.
